How to make an object fade out from one end?
You can use an object as mapping coordinate for a coloramp, and by moving it around you can tune up the effect or transparency which is obtained by mixing a transparent and a diffuse shader in this case. Just an example.


You can also use the generated mapping coordinate depending on your geometry. In the last picture i had put the object used for mapping a little backward in the scene. Here the input is a texture coordinate node and the mapping is slided on x